Space of modular forms of level 27 and weight 11

• Label: 27.11
• Level: 27
• Weight: 11
• Dimension: 205
• Nonzero newspaces: 3
• Newform subspaces: 6
• Sturm bound: 594
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 27 = 3^{3} \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(594\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(27))\).

	Total	New	Old
Modular forms	285	221	64
Cusp forms	255	205	50
Eisenstein series	30	16	14

Trace form

205 * q - 3 * q^2 - 6 * q^3 - 1445 * q^4 - 9921 * q^5 + 18234 * q^6 - 2251 * q^7 - 9 * q^8 + 119124 * q^9 + 118203 * q^10 - 1947 * q^11 - 1015107 * q^12 + 1085009 * q^13 + 4269147 * q^14 - 2548539 * q^15 - 5220893 * q^16 - 9 * q^17 + 6676947 * q^18 + 2961788 * q^19 + 1382619 * q^20 - 21049824 * q^21 + 4763667 * q^22 + 18382074 * q^23 + 87359400 * q^24 - 30114521 * q^25 - 60562494 * q^27 - 32040310 * q^28 + 49204824 * q^29 + 216153117 * q^30 - 61387645 * q^31 - 88960311 * q^32 - 198927081 * q^33 + 68254983 * q^34 - 260153622 * q^35 + 199074744 * q^36 + 241950578 * q^37 + 872307201 * q^38 + 152777949 * q^39 - 291257781 * q^40 - 1290257895 * q^41 - 1627952634 * q^42 - 256662289 * q^43 + 2245906431 * q^44 + 1041263847 * q^45 + 1034553165 * q^46 - 1396552593 * q^47 - 1664196711 * q^48 + 243627225 * q^49 + 633323244 * q^50 + 1007158626 * q^51 - 3934516009 * q^52 - 1206704682 * q^54 + 2976295686 * q^55 + 12087321 * q^56 - 1000586442 * q^57 - 1546680345 * q^58 - 1259431401 * q^59 + 1176655374 * q^60 - 4606895863 * q^61 + 2786630112 * q^62 + 2270781765 * q^63 + 18213872389 * q^64 + 8132984925 * q^65 - 5594499243 * q^66 - 3043478038 * q^67 - 10057534110 * q^68 - 7767764199 * q^69 - 11450703309 * q^70 - 5512912173 * q^71 - 15991303644 * q^72 + 12362794889 * q^73 + 52110403707 * q^74 + 15296936925 * q^75 + 2257486991 * q^76 - 27704034489 * q^77 - 12511026108 * q^78 - 4245017005 * q^79 + 440880768 * q^81 + 28601897622 * q^82 + 31066927863 * q^83 - 31766160684 * q^84 - 19384067907 * q^85 - 72352863939 * q^86 - 10927113525 * q^87 + 4648657227 * q^88 + 34430237370 * q^89 + 12602186028 * q^90 + 38947403245 * q^91 + 81165252693 * q^92 + 57140838285 * q^93 - 53592094113 * q^94 - 34440428625 * q^95 - 78182924274 * q^96 - 600622336 * q^97 - 103117506282 * q^98 - 72892391589 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(27))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
27.11.b	\(\chi_{27}(26, \cdot)\)	27.11.b.a	1	1
		27.11.b.b	2
		27.11.b.c	4
		27.11.b.d	6
27.11.d	\(\chi_{27}(8, \cdot)\)	27.11.d.a	18	2
27.11.f	\(\chi_{27}(2, \cdot)\)	27.11.f.a	174	6

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)